Question

A fraction becomes 8÷11,if 3 is added to both the numerator and deniminator, also if 3 is subtracted from the numerator and the denominator it becomes 2÷5. find the fraction​

Answer 1

Answer:

The Original Fraction is 5/8.

Step-by-step explanation:

Let the Numerator be N and,

Denominator be D.

A.T.Q.

(N+3)/(D+3)=8/11

By Cross Multiplication,

➟ 11(N + 3) = 8(D + 3)

➟ 11N + 33 = 8D + 24

➟ 11N - 8D = 24 - 33

➟ 11N - 8D = - 9 ⠀⇒⠀(¡)

Again,

(N-3)/(D-3)=2/5

By Cross Multiplication.

➟ 5(N - 3) = 2(D - 3)

➟ 5N - 15 = 2D - 6

➟ 5N - 2D = - 6 + 15

➟ 5N - 2D = 9 ⠀⇒⠀(¡¡)

Multiplying (¡¡) by 4.

➟ 4(5N - 2D) = 4 × 9

➟ 20N - 8D = 36 ⠀⇒⠀(¡¡¡)

From Equation (¡) and (¡¡¡)

⟹ 20N - 8D = 36

⟹ 11N - 8D = - 9

⟹ 9N = 45

⟹ N=45/9

⟹ N=5

Plugging the Value of N in Eq. (¡)

⟹ 11N - 8D = - 9

⟹ (11 × 5) - 8D = - 9

⟹ 55 - 8D = - 9

⟹ - 8D = - 9 + 55

⟹ 8D = 64

⟹ D=64/8

⟹ D=8